Could a heart of darkness power pair-instability supernovae?

Title: Dark Matter Annihilation and Pair-Instability Supernovae

Authors: Djuna Croon and Jeremy Sakstein

First Author’s Institution: Institute for Particle Physics Phenomenology, Department of Physics, Durham University

Status: Published in Physical Review D [closed access]

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Stars are perpetual explosions that exist in an extremely delicate balance. Gravity is constantly trying to crush the star into a black hole while the radiation pressure emitted by the core’s nuclear fusion desperately prevents collapse. However, if a star is big enough (see Figure 1), it may produce photons that have enough energy to split into an electron and a positron pair.

This means the photon cannot contribute to the radiation pressure, and the star has made a fatal error. This lapse allows gravity to briefly overcome radiation pressure; the star partially collapses before runaway nuclear fusion creates a thermonuclear explosion: a so-called (and hitherto theoretical) Pair Instability Supernova.

Today’s authors took a look at this dramatic tale and decided it simply needed more spice, so they gave our main character a secret: a dark matter core. Could this heart of darkness help explain the black hole mass gap, and could we spot the signatures of a dark matter-powered supernova as a smoking gun that finally reveals the identity of the ever-mysterious dark matter?

Dark Matter, Bright Star

So how would dark matter affect these massive stars’ supernovae? Well, being massive objects, stars could theoretically capture dark matter from their surrounding environment via their force of gravity. When that dark matter gets pulled into the star, it can find its respective anti-particle and annihilate with it, releasing a burst of energy. This means that dark matter could “inject” energy deep into the core of a star. (It has even been postulated that a star could be powered entirely by dark matter, a dark star, which I think holds the record for most oxymoronic name of all time.) The authors set out to determine how this extra juice could affect these stars and their supernovae.

In order to figure out where the energy ends up, we need to determine where the dark matter is. The authors turn to a stellar dynamics simulation code (called MESA) in order to solve this problem. To do so, they set up a few key ground rules. They assume that the dark matter is in thermal equilibrium with the star (i.e. the dark matter is the same temperature as the star) and that the dark matter isn’t escaping the star. They also assume that the dark matter is in capture-annihilation equilibrium. This means the star sucks in dark matter at the same rate as it is annihilated within the star, so that the amount of dark matter in the star remains constant over time. Taking all of these assumptions yields an equation for how much energy is deposited in the star by dark matter at different distances from the center. This equation depends on a bunch of complicated physics and therefore relies on a ton of different factors, such as the mass and number density of the dark matter particle, the radial profile of the star, and the likelihood of a dark matter annihilation reaction (measured via the cross section). The authors modified their stellar evolution model to include this equation in it. 

Shifting the Supernova Scene

In order to determine how dark matter energy injection would affect stellar physics, the authors first ask: how much would a star need to be messed with to make it undergo a pair instability supernova? This kind of supernova needs a specific combination of density and temperature, so if a star finds itself in this special spot on a graph of density versus temperature (called the ρ–T plane) it might explode. As a star evolves, it wanders through different combinations of densities and temperatures, following a “stellar track” (see Figure 2) in the ρ–T plane.

The authors find that the injection of energy by dark matter needs to be strong enough to significantly affect the equation of state of the star. This has big ramifications for how dark matter might affect the star. The authors predict that heavy dark matter (side note: by heavy we mean a heavier dark matter particle. Technically, we don’t even know if dark matter is a particle but we’ve got to start somewhere!) would sink towards the core of the star, where the energy it’s injecting has to compete with the nuclear engine at the core of the star. Therefore, heavy dark matter is unlikely to change the stellar dynamics until after the nuclear furnace begins to weaken, roughly after the star has burned up all of its helium. Lighter dark matter will not sink as much, ending up on the outskirts of the star, where there is less nuclear fusion. Because of this, the energy that dark matter puts into the star could dominate in this region, which could significantly affect the star’s tracks through the ρ–T plane. 

With these theoretical considerations in hand, we can crunch some numbers in a simulation! The authors simulate stars with masses between 40 and 90 solar masses, two masses of dark matter particles, and a variety of dark matter number densities. They assume the dark matter has an initial velocity of 220 km/s: the speed dark matter would pass us by as our Solar System orbits through the Milky Way. 

The simulations showed very interesting results. For the heavier dark matter particle, it did indeed sink to the center of the star as predicted. There, its energy injection could help supplement the energy of the nuclear furnace, allowing its Helium “fuel” to last longer. This allowed the star more time to undergo an interaction that processes Carbon into Oxygen, which results in a more violent explosion. Because of this, the final resulting black hole tends to be of lower mass because more stellar material was simply blasted away, see Figure 3. This has an effect of lowering the bottom edge of the black hole mass gap.

On the other hand, the lighter dark matter particle remained spread out in the outer layers of the star, as previously predicted. This meant its energy injection could help support the star without allowing it to contract, preventing the Carbon to Oxygen process we saw in the previous case. This injected energy in the outer layers also causes the star to expand, reducing pressure and density, sometimes enough to completely avoid pair instability supernova! Because of this, the star survives to a ripe old age where it can undergo the boring passé core-collapse supernovae. Since this star made it all the way to core-collapse with the help of dark matter, it results in a more massive black hole than expected by the standard model, see Figure 3. This results in a mass gap forming at higher masses.

These results mean that one could hypothetically try to infer the mass of dark matter particles by looking at the edges of the mass gap in gravitational wave data. Our authors are quick to point out that these effects on the edges of the mass gap are subtle, and are likely not yet detectable with current generation gravitational wave detectors. However, today’s paper shows the incredible web of physics that makes up our universe. Think about it: in this example, dark matter affected stellar physics, which then affected supernova physics, which changes the black hole masses, all of which had to be measured through gravitational waves! Today’s paper not only shows an incredibly interesting new way to think about and study dark matter, but also shows us that the trick to finally cracking the secrets of the universe could be found in places you might not at first think to look. 

Astrobite edited by Junellie Gonzalez Quiles

Featured image credit: Wikimedia Commons